Article · Scientific works/Elmi eserler · June 22, 2026
LORENTZ-TYPE THEOREMS IN LIPSCHITZ CLASSES
Askhat Birlesovich Mukanov, Zhalgas Mukanov
Abstract
We investigate the relationship between the smoothness properties of functions and the asymptotic behavior of their Fourier transforms. We focus on how various notions of regularity and smoothness influence the rate of decay of the Fourier transform at infinity. Special attention is given to the class of functions whose Fourier transforms satisfy a general monotonicity condition. Within this framework, we establish a Lorentz-type characterization theorem that connects smoothness estimates of functions with precise decay properties of their Fourier transforms. Our results extend several classical statements in harmonic analysis and provide new criteria for describing function classes through the behavior of Fourier transforms.
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